An electron has intrinsic spin angular momentum S= hbar/2. The spin magnetic moment is mu_s=-g_s e/2m_eS. Given g_s=2.0023, what is |mu_s| in units of the Bohr magneton mu_B= ehbar/2m_e?

An electron has intrinsic spin angular momentum $S = \frac{hba r}{2}$ . The spin magnetic moment is $m u_{s} = - g_{s} \frac{e}{2 m _{e}} S$ . Given $g_{s} = 2.0023$ , what is $∣ m u_{s} ∣$ in units of the Bohr magneton $m u_{B} = \frac{e hba r}{2 m _{e}}$ ?

easy MCQ 1 mark Class 12 · Physics · Atoms

a) 1.0012 µ_B
b) 1.0024 µ_B
c) 1.0046 µ_B
d) 1.0088 µ_B

Answer

a) 1.0012 µ_B

The correct answer is a) 1.0012 µ_B — Step 5: Compute $g_{s} \frac{1}{2} = 2.0023 \times 0.5 = 1.00115$ and round to four significant figures giving $1.0012, μ_{B}$ .

Step-by-step solution

Step 1: Substitute $S = \frac{hba r}{2}$ into $m u_{s} = - g_{s} \frac{e}{2 m _{e}} S$ to obtain $m u_{s} = - g_{s} \frac{e}{2 m _{e}} \frac{hba r}{2}$ .
Step 2: Simplify the expression to $m u_{s} = - g_{s} \frac{e hba r}{4 m _{e}}$ .
Step 3: Recognize that $m u_{B} = \frac{e hba r}{2 m _{e}}$ , hence $\frac{e hba r}{4 m _{e}} = \frac{1}{2} m u_{B}$ .
Step 4: Take the magnitude $∣ m u_{s} ∣ = g_{s} \frac{1}{2} m u_{B}$ .
Step 5: Compute $g_{s} \frac{1}{2} = 2.0023 \times 0.5 = 1.00115$ and round to four significant figures giving $1.0012, μ_{B}$ .

Common mistake: Using

∣ m u_{s} ∣ = g_{s} m u_{B}

instead of

g_{s} /2

factor

Concept tested: Spin magnetic moment in Bohr magneton

Published 12 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

← All Atoms questions

An electron has intrinsic spin angular momentum S=2hbar​. The spin magnetic moment is mus​=−gs​2me​e​S. Given gs​=2.0023, what is ∣mus​∣ in units of the Bohr magneton muB​=2me​ehbar​?

Step-by-step solution

An electron has intrinsic spin angular momentum $S = \frac{hba r}{2}$ . The spin magnetic moment is $m u_{s} = - g_{s} \frac{e}{2 m _{e}} S$ . Given $g_{s} = 2.0023$ , what is $∣ m u_{s} ∣$ in units of the Bohr magneton $m u_{B} = \frac{e hba r}{2 m _{e}}$ ?